The next number in the sequence 16, 4, 20, 24, 44 is 68 and in the sequence 6, 5, 15, 10, 70 is 61.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
Now the given series are,
16, 4, 20, 24, 44
and 6, 5, 15, 10, 70
Now the difference between the two terms of the series 16, 4, 20, 24, 44
4 - 16 = 12 = 4*3
20 - 4 = 16 = 4*4
24- 20 = 4 = 4*1
44 - 24 = 20 = 4*5
So let x be the next term; hence it can be written as
x - 44 = 4*6
x = 24 + 44
x = 68
Now for the series 6, 5, 15, 10, 70, it is an alternative series,
6 - 1 = 5
5 x 3 = 15
15 - 5 = 10
10 x 7 = 70
So the next term is given as,
70 - 9 = 61
Hence, The next number in the sequence 16, 4, 20, 24, 44 is 68 and in the sequence 6, 5, 15, 10, 70 is 61.
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Stephen Had $1200. He spent 40% of it. How much money did he spend?
[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4\\\\40\%\ of\ \$1200\ is\ 0.4\cdot\$1200=\$480\\\\Answer:\ \text{He spend}\ \$480.[/tex]
Final answer:
To determine the amount Stephen spent from his $1200 at 40%, the percentage is converted to a decimal (0.40) and multiplied by $1200, resulting in $480 spent.
Explanation:
Stephen had $1200. To calculate the amount of money he spent after using 40% of his money, we need to find 40% of $1200. We can write this as 0.40 × $1200.
Step 1: Convert the percentage into a decimal: 40% = 0.40
Step 2: Multiply the decimal by the total amount of money Stephen had: 0.40 × $1200 = $480.
Hence, Stephen spent $480 out of his $1200.
how do u solve 1736÷56 step by step
Answer:
31
Step-by-step explanation:
use a step by step calculator.
What is the largest fraction 3/4 7/8 8/10 7/9?
Answer:
7/8 ths
Step-by-step explanation:
3 divided by 4 is .75
* 7 divided by 8 is .875
8 divided by 10 is .80
7 divided by 9 is .77
If you divide the fractions you can compare the values and the highest value is your largest fraction.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator. The fraction 7/9 has the largest fraction.
Given information-
The set of the fraction given in the problem is,
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
What is the order of fraction?The order of the fraction is arranging the fraction number from the smallest to the largest number.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator.
To compare the fraction, make the denominator with same.
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
To make the denominator same find out the least common factor of denominators which are 4,8,10 and 9 which is 360.
Multiply and divide with 360 in the given fractions to bring the 360 in denominator,
[tex]\dfrac{3\times360}{4\times360}, \dfrac{7\times360}{8\times360}, \dfrac{8\times360}{10\times360}, \dfrac{7\times360}{9\times360}[/tex]
[tex]\dfrac{270}{360}, \dfrac{315}{360}, \dfrac{288}{360}, \dfrac{315}{360}[/tex]
As the numerator 315 is the highest among all. Hence the fraction 7/9 has the largest fraction.
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what is 3a2(ab2+b2) =
Answer: 3a^3 b^2+3a^2 b^2
Step-by-step explanation:
3a^2(ab^2+b^2)
=(3a^2)(ab^2+b^2)
=(3a^2)(ab^2)+(3a^2)(b^2)
=3a^3 b^2+3a^2 b^2
hope this helps
please mark brainliest answer
Answer:
3a3b2 + 2a2b2
Step-by-step explanation:
3a2(ab2 + b2) =
= 3a2*ab2 + 3a2*b2
= 3a3b2 + 2a2b2
solve
4x+6<-6
I could really use the help
Answer:
x < -3
Step-by-step explanation:
First subtract 6 from both sides of the inequality.
[tex]4x+6-6<-6-6[/tex]
[tex]4x<-12[/tex]
Divide 4 on both sides.
[tex]\frac{4x}{4} < \frac{-12}{4}[/tex]
[tex]x<-3[/tex]
The coordinates of point P are (-3, 5). Point R is a reflection of point P across the x-axis. Point S is a reflection of point P across the y-axis.
Point R is located in quadrant . Point S is located in quadrant .
Answer:
R is in the third quadrant and S is in the first quadrant
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
P(- 3, 5 ) → R(- 3, - 5 ) ← third quadrant
Under a reflection in the y-axis
a point (x, y ) → (- x , y )
P(- 3, 5 ) → S(3, 5 ) ← first quadrant
In a reflection across the x-axis, the y-coordinate is negated, and in a reflection across the y-axis, the x-coordinate is negated. Thus, Point R (-3, -5) from point P (-3, 5) is in the fourth quadrant and Point S (3, 5) is in the first quadrant.
Explanation:The given point P has the coordinates (-3, 5). When a point is reflected across the x-axis, the y-coordinate changes its sign. So, the reflection of point P across the x-axis (Point R) would be at (-3, -5). This places Point R in the fourth quadrant.
Similarly, when a point is reflected across the y-axis, the x-coordinate changes its sign. Therefore, the reflection of point P across the y-axis (Point S) would be at (3, 5). This places Point S in the first quadrant.
In summary, Point R is located in the fourth quadrant and Point S is located in the first quadrant.
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solve the inequality -8x-10>7x+20
Answer:
-2 > x
Step-by-step explanation:
-8x-10>7x+20
Add 8x to each side
-8x+8x-10>7x+8x+20
-10 > 15x+20
Subtract 20 from each side
-10 -20 > 15x+20-20
-30 > 15x
Divide by 15
-30/15 > 15x/15
-2 > x
The graph shows the number of people infected with a virus as a function of time.
The graph shows exponential ___
A- decay
B- growth
As the amount of people infected with the virus decreases, time ___
A- increases
B- decreases
The graph shows exponential B
exponential decay is when the graph is decreasing/going down
exponential growth is when the graph is increasing/going up
The graph is shown to be increasing, so it is exponential growth
As the amount of people infected with the virus decreases, time B
If you look at the graph, as time increases, the number of infected people also increases. So when the # of infected ppl decreases, so does time
Answer:
1. Growth
2. Decreases
Step-by-step explanation:
The graph shows the number of people infected with a virus as a function of time.
1.
The graph shows exponential growth because the graph is increasing above. It is going upwards, as the time is increasing.
2.
As the amount of people infected with the virus decreases, time decreases.
As it is a growth graph, if we study this in the opposite direction, that is from upwards to downwards, we can see that as the graph is going down, the values on the y axis are also decreasing.
What division problem does this model represent
whats is the ratio of 3 dogs to 4 cats
Answer:
3 to 4
or
3:4
Step-by-step explanation:
if f(x)=x^2-x and g(x)=x+1, determine f (g(x)) in simplest from
Answer:
f(g(x)) = x^2 +x
Step-by-step explanation:
To find f(g)(x) , we substitute g(x) in for x in the function f(x)
f(x) = x^2 -x
f(g(x)) = g(x)^2 -g(x)
= (x+1)^2 - (x+1)
= (x+1)*(x+1) - (x+1)
FOIL the square
(x+1) (x+1)
First x*x = x^2
outer x*1 = x
inner 1*x = x
last 1*1 =1
Add them together
x^2 + x+x+1 = x^2+2x+1
f(g(x)) = (x+1)*(x+1) - (x+1)
= x^2+2x+1 -(x+1)
Distribute the -1
= x^2 +2x+1 -x-1
= x^2 +x
f(g(x)) is basically replacing the x with g(x).
So, f(x)=(g(x))^2 - g(x)
g(x), in turn, equals x+1
Replace g(x) with x+1
(x+1)^2 - (x+1)
Expand: x^2+x+x+1 - x - 1
Cancel out x and 1
f(g(x))=x^2+x
If you require factoring it's
f(g(x))=x(x+1)
As the figure shows Elton runs 500 m to point b first then he turns 100 degrees and runs another 350 m to point c how far is the distance from point a to c
Answer:
658.24 m
Step-by-step explanation:
Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:
[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]
Answer:
658.24 m
Step-by-step explanation:
The figure makes a triangle with vertices abc.
Where ab = 500 m
bc = 350 m
The angle abc = 100°
Using the cosine rule we can find the distance ac.
ac² = 500²+350² - 2×500×350×cos100°
= 372,500 - -60,776.86
= 433,276.86
ac = √433,276.86
= 658.24 m
which order pairs are solutions of the inequality -7y +2x ≤ 3
A (0,0)
B (1,1)
C (-3,5)
Answer: A & B
Step-by-step explanation:
-7y + 2x ≤ 3
(0, 0): -7(0) + 2(0) ≤ 3
0 + 0 ≤ 3
0 < 3 TRUE
(1, 1): -7(1) + 2(1) ≤ 3
-7 + 2 ≤ 3
-5 < 3 TRUE
(-3, 5): -7(-3) + 2(5) ≤ 3
21 + 10 ≤ 3
31 < 3 FALSE
In a regular deck of cards calculate the probability that a face card is drawn given that it is a heart
nevermind it the answer is D=0.23 or 23%
Answer:
Option 4) Probability = 30%
Step-by-step explanation:
We are given the following information:
We have a deck of cards.
We have to find the probability of drawing a face card given that is a heart.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
Conditional probability:
The probability of happening of event A given event B:
[tex]P(A|B) = \displaystyle\frac{P(A \cap B)}{P(B)}[/tex]
[tex]P(\text{Face card}|\text{Hearts}) = \displaystyle\frac{P(\text{Face card} \cap \text{Hearts})}{P(\text{Hearts)}}\\P(\text{Hearts}) = \displaystyle\frac{13}{52}\\\\P(\text{Face card} \cap \text{Hearts}) = \frac{4}{52}\\\\P(\text{Face card}|\text{Hearts}) = \frac{4/52}{13/52} = \frac{4}{13}\\\\=\frac{4}{13}\times 100\% = 30.77\%[/tex]
Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 65 miles per hour to and from the park.
Choose and solve the inequality that represents the possible distances from Alexandria’s home to a park that satisfies the conditions above.
Answer:
The correct answer for this problem is 200 miles.
Solve, using the substitution method.
y = 2x + 6
3x – y = 6
There are an infinite number of solutions.
(12, 30)
(14, 12)
There is no solution.
The solution to the system of equations is (12, 30).
Option B is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the system of equations using the substitution method,
We solve one equation for one of the variables and substitute the expression into the other equation.
Let's solve the first equation for y:
y = 2x + 6
Now, substitute y = 2x + 6 into the second equation and solve for x:
3x - y = 6
3x - (2x + 6) = 6
3x - 2x - 6 = 6
x = 12
Now that we have found x, we can substitute it back into either of the original equations to find y.
Let's use the first equation:
y = 2x + 6
y = 2(12) + 6
y = 30
Therefore,
The solution to the system of equations is (12, 30).
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Line segment AB has endpoints A(1,4) and B(6,2). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 2:3
Answer:
[tex](3,3\frac{1}{5})[/tex]
Step-by-step explanation:
We use the formula;
[tex](\frac{mx_2+nx_1}{2},\frac{my_2+ny_1}{2})[/tex]
where m:n=2:3 and [tex]x_1=1,x_2=6,y_1=4,y_2=2[/tex]
We substitute these values to get;
[tex](\frac{2(6)+3(1)}{2+3},\frac{2(2)+3(4)}{2+3})[/tex]
We simplify to get:
[tex](\frac{15}{5},\frac{16}{5})[/tex]
[tex](3,3\frac{1}{5})[/tex]
Answer:
(3,16/5)
Step-by-step explanation:
(2)(6)+(3)(1)/(2+3),(2)(2)+(3)(4)/(2+3)=3,16/5
Use synthetic division to solve (4x3-3x2+5x+6)/(x+6). What is the quotient?
Answer:
[tex]\text{The quotient is }4x^2 -27x +167[/tex]
Remainder is -996
Step-by-step explanation:
[tex]\text{Given the polynomial }4x^3-3x^2+5x+6\text{ which is to be divided by }x+6[/tex]
we have to find the quotient using synthetic division
x+6 =0 , so x=-6
We divide by -6.
The steps for synthetic division are
Step 1: Set up the synthetic division.
Step 2: Put down the leading coefficient to bottom row.
Step 3: Multiply divisor which is on left by the value just written on the bottom row.
Step 4: Add the column created in above step.
Step 5: continue until we reached last column.
The synthetic division is shown in attachment.
[tex]\text{The quotient is }4x^2 -27x +167[/tex]
Remainder is -996
When you divide 4x³- 3x² + 5x + 6 by (x+6) using synthetic division, the quotient is 4x²- 27x + 162
To divide ([tex]4x^3-3x^2+5x+6[/tex]) by (x+6) using synthetic division, follow the steps provided.
Arrange the terms of the dividend in descending order of degree, filling in any missing terms with a coefficient of 0.
Set up the synthetic division table with the divisor (x+6) as the divisor and the coefficients of the dividend (4, -3, 5, 6) as the dividend.
Perform the synthetic division:
Bring down the first coefficient, 4.
Multiply the divisor (x+6) by the value in the bottom row of the divisible column (which is 4).
The result is written in the next row.
Add the value in the next row to the coefficient in the next column and write the sum in the next row.
Repeat this process until all rows are completed.
The numbers in the bottom row of the table represent the coefficients of the quotient.
The quotient for this division is [tex]4x^2 - 27x + 167.[/tex]
Therefore, the quotient of ([tex]4x^3-3x^2+5x+6[/tex])/(x+6) is [tex]4x^2 - 27x + 167.[/tex]
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The five fifth grade teachers ans six fourth grade teachers ordered 2 large pizzas all together. Each pizza costs $13.75. If they are going to spilt the cost evenly, how much will each person need to pay?
Answer:
80 Cents
Step-by-step explanation:
Answer: Each person will need to pay $1.25
Step-by-step explanation: $13.75 divided by the 11 people = $2.25
Perhaps brainliest?
This is the graph of f(x). What is the value of f(2)?
Look at the picture.
f(2) = 8 or f(2) = 9Answer: f(2) = 9From the graph, the value of the function at x = 2 will be 9. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The graph of the function is shown.
From the graph, the value of the function at x = 2 will be 9.
Then the correct option is B.
More about the function link is given below.
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Find the unit rate to the nearest cent per ounce.
A 24-ounce box of cornflakes costs $4.59
Answer:
0.19125
Step-by-step explanation:
You divided 4.59 by the amount 24-oz
Is this a true proportion ? 3/4,8/12
Question
Is this a true proportion ? 3/4,8/12
Answer:
FalseStep-by-step explanation:
3/4 = 8/12
semplify
3/4 = 2/3
or you can solve in this way
3/4 = 8/12
0.75 = 0.66≈
what is the sum of 121/4+5 5/6 reduced to lowest terms thanks
Answer:18 1/12
Step-by-step explanation:i first added the whole numbers 12 and 5 to get 17; i then addled 1/4 and 5/6; i did this by finding a common denominator of both fractions and converted them into 6/24 and 20/24; i added them to get 26/24 which simplifies to 1 and 2/24, which equals 1 1/12; i added 1 to 17 and got 18, then added 1/12 to get 18 1/12
The sum of 121/4 and 5 5/6 is found by converting the mixed number to an improper fraction, finding a common denominator, adding the fractions, and simplifying if possible. The final answer is 433/12, which is already in its lowest terms.
The question asks for the sum of the numbers 121/4 and 5 5/6 reduced to the lowest terms. To answer this, we must first convert the mixed number to an improper fraction and then add it to the other fraction. Here's how to do it step by step:
Convert 5 5/6 to an improper fraction: 35/6.
Add 121/4 to 35/6. To do this, find a common denominator, which would be 12 in this case.
Convert both fractions to have the common denominator: 121/4 becomes 363/12, and 35/6 becomes 70/12.
Add the two fractions: 363/12 + 70/12 equals 433/12.
Reduce the fraction if possible. In this case, 433/12 is already in its lowest terms.
Therefore, the sum of 121/4 and 5 5/6 reduced to lowest terms is 433/12.
y^-9*y^-8*y^10= (its algebra 2 and i cant figure it out it please help)
[tex]Use:\\\\a^n\cdot a^m=a^{n+m}\\\\y^{-9}\cdot y^{-8}\cdot y^{10}=y^{-9+(-8)+10}=y^{-7}[/tex]
You are the new warehouse manager and you have a facility that has 25 storage racks that are 25 feet long, 12 feet high and 3 feet wide. The boxes that you need to store are 15x8x10 inches and there are 5000 of the boxes. Do you have enough storage space?
Answer is shown in the attached image, in RED.
What is the awnser for 1/2 x + 8 equals 16
Answer:
What do mean by equals 16?
Step-by-step explanation:
1/2x+8=16
1/2x=16-8
1/2x=8
x=8:1/2
x=8*2
x=16
Hope this helps! <3
Determine the type of triangle that has angle measurements of 45°, 45°, 90°.
Answer:
I might be wrong but i think it is 90 Degree Angle
Step-by-step explanation:
Answer:
right triangle
Step-by-step explanation:
90 degrees is a right angle so it will be a right triangle
guys I need help.....
Answer:
.224 / 7 = .032
Step-by-step explanation:
.224 / 7
7 goes into 2 0 times with 2 left over
7 goes into 22 3 times with 1 left over
7 goes into 14 2 times with 0 left over
.224 / 7 = .032
Answer:
.032
Step-by-step explanation:
Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions. f(x) = 4x2 − 25 g(x) = 4x2 + 25 h(x) = 3x2 − 25
Rational root theorem is used to determine the possible root of a function.
Rational root theorem provides a complete list of all roots of [tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex][tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 - 25 = 0}[/tex]
Add 25 to both sides
[tex]\mathbf{4x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = \frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm\frac{5}{2}}[/tex]
The function has rational roots.
This means that: rational root theorem provides a complete list of all roots
[tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 + 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{4x^2 = -25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = -\frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm \sqrt{-\frac{25}{4}}}[/tex]
The function has complex roots.
This means that: rational root theorem does not provide a complete list of all roots
[tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{3x^2 - 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{3x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = 8.333}[/tex]
Take square roots
[tex]\mathbf{x = \pm 2.89}[/tex]
The function has irrational roots.
This means that: rational root theorem does not provide a complete list of all roots
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Explanation of the Rational Root Theorem and its application to polynomial functions f(x), g(x), and h(x).
The Rational Root Theorem provides a list of possible rational roots for a polynomial function. However, it does not guarantee that all roots will be rational. Let's examine the given polynomial functions:
For f(x) = 4x² - 25: The rational root theorem suggests possible rational roots, but the roots could also be irrational.For g(x) = 4x² + 25: As this polynomial has no real roots (due to the presence of complex numbers under the square root), the rational root theorem won't provide all roots.For h(x) = 3x² - 25: Again, the rational root theorem gives possible rational roots, but not the complete list of roots.A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Answer : The value of car will be, $11654.98
Step-by-step explanation:
Given,
Principle = $22300
Time = 6 years
Rate of depreciation = 10.25 %
Formula used :
[tex]A=P(1-\frac{R}{100})^t[/tex]
where,
A = amount
P = principle
R = rate of depreciation
T = time
Now put all the given values in the above formula, we get:
[tex]A=P(1-\frac{R}{100})^t[/tex]
[tex]A=\$ 22300(1-\frac{10.25}{100})^{6}[/tex]
[tex]A=\$ 11654.98[/tex]
Therefore, the value of car will be, $11654.98